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Simplifying (12 + -1y) * y = 40 Reorder the terms for easier multiplication: y(12 + -1y) = 40 (12 * y + -1y * y) = 40 (12y + -1y2) = 40 Solving 12y + -1y2 = 40 Solving for variable 'y'. Reorder the terms: -40 + 12y + -1y2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 12y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 40 + -12y + y2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -12y + -40 + y2 = 0 + -40 Reorder the terms: 40 + -40 + -12y + y2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -12y + y2 = 0 + -40 -12y + y2 = 0 + -40 Combine like terms: 0 + -40 = -40 -12y + y2 = -40 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = -40 + 36 Reorder the terms: 36 + -12y + y2 = -40 + 36 Combine like terms: -40 + 36 = -4 36 + -12y + y2 = -4 Factor a perfect square on the left side: (y + -6)(y + -6) = -4 Can't calculate square root of the right side. The solution to this equation could not be determined.
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